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Proof step 9 from proof validrefs-maxlen (previous step)

st[r -- mkfs(class, ty1, fieldvar) '] = refval(r0), validrefs(str, r0 ' + refs, ty1, st), mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), st[r -- _type] .type ≤ ty, # st .refs ≤ # refs, is_obj(str, r, st) ⊦ r = r0, r = jvmref, validrefs(str, r0 ' + refs, ty1, st -- r), r ∈ refs, r0 ∈ refs, dups(refs)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ validrefs(str, refs, ty, st) ∧ ¬ r ∈ refs → validrefs(str, refs, ty, st -- r)

Rule argument

[crewrite-arg: validrefs-delete-03 , F , [r, st, ty, refs, str] → [r, st, ty1, r0 ' + refs, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ≠ r0 → (r ∈ r0 ' + refs ↔ r ∈ refs)])], [EXTRATERMS : (r, st, ty1, r0 ' + refs, str)]]